Chapter 1 Introduction
1.1 An overview of inverse problems
1.1.1 Definition and applications of inverse problems
1.1.2 Ill-posedness and the regularization methods
1.2 Recent developments of inverse scattering and inverse source prob-lems
1.2.1 Inverse scattering problems
1.2.2 Inverse source problems
1.2.3 Relevant numerical methods
1.3 The direct sampling method
1.4 The contributions of the thesis
1.5 Thesis organization
Chapter 2 Inverse acoustic source problem
2.1 Introduction and preliminaries
2.1.1 Bessel functions
2.1.2 Model setup of the inverse source problem
2.2 The direct sampling method
2.2.1 Theoretical results in 2D
2.2.2 Theoretical analysis in 3D
2.2.3 The inversion algorithm
2.3 Numerical results
2.3.1 Two dimensional examples
2.3.2 Three dimensional simulations
2.4 Brief summary
Chapter 3 Inverse electromagnetic source problem
3.1 Model problem
3.2 The direct sampling method and theoretical analyzes
3.2.1 The near-field data
3.2.2 The far-field data
3.3 Numerical results
3.3.1 Examples using the near-field data
3.3.2 Simulations using the far-field data
3.4 Brief summary
Chapter 4 Inverse elastic source problem
4.1 The governing equations of the problem
4.2 The direct sampling method
4.2.1 Theoretical results in 2D
4.2.2 Theoretical analysis in 3D
4.2.3 Stability result
4.3 Numerical results
4.4 Brief summary
结论
Conclusion
参考文献
List of Publications
声明
致谢
Resume
哈尔滨工业大学;
